In order to support the anytime abort requirements of a manned mission to the Moon, the vehicle abort capabilities for the translunar and circumlunar phases of the mission must be studied. Depending on the location of the abort maneuver, the maximum return time to Earth and the available propellant, two different kinds of return trajectories can be calculated: direct and fly-by. This paper presents a new method to compute these return trajectories in a deterministic and fast way without using numerical optimizers. Since no simplifications of the gravity model are required, the resulting trajectories are very accurate and can be used for both mission design and operations. This technique has been extensively used to evaluate the abort capabilities of the Orion/Altair vehicles in the Constellation program for the translunar phase of the mission
